คลังความรู้

The discussion addresses a backtest in which a mean-reversion pairs strategy scales positions as the spread moves farther from its mean. Its central recommendation is to track daily profit and loss in currency terms, reflecting the strategy’s actual position…

The discussion examines the claim that a long calendar spread’s maximum loss is limited to its opening debit when the short option expires. In the usual intuition, if the underlying moves far below the strike, both calls lose value; far above it, both…

The discussion considers whether a constant displacement can adapt a standard LIBOR market model to negative interest rates. It proposes applying the shift to the forward rates used in the diffusion and drift numerators, while the accepted response clarifies…

This explanation distinguishes an ETF’s reporting or base currency from the currencies of the assets it holds. Using a Japan equity fund as an example, it says the fund owns Japanese yen-denominated stocks and converts their value into US dollars for daily…

The document works through the variance of a weighted basket when all asset returns have correlation one. For two assets, it writes the usual portfolio variance expression, including the covariance term, and recognizes that the expression becomes the square…

The document discusses how to calculate a one-year PRIIPs category 2 stress scenario for the Euro Stoxx 50 and why the reported value can change sharply between monthly KID dates. The response says the stress volatility should be based on rolling 21-day…

The document considers forecasting actual high-frequency prices, including bid and ask quotes, rather than forecasting volatility. It highlights practical challenges: model validity may be brief, validity is difficult to assess, and computationally expensive…

The discussion clarifies the difference between a cross-currency swap and a cross-currency basis swap, then illustrates how a basis swap can convert a foreign-currency bond exposure into a USD funding comparison. In the example, an investor exchanges USD…

The document raises whether the price of a call or put butterfly can indicate the likelihood that a stock will finish near the butterfly’s middle strike. It questions a casual explanation based on at-the-money option delta and asks how to construct an…

A non-deliverable interest rate swap exchanges fixed and floating interest cash flows linked to one local currency, but settles the net amount in a deliverable currency such as USD or EUR. The example describes paying a fixed local-currency rate and…

The discussion derives the distribution of a future asset price under geometric Brownian motion and clarifies the relationship between the distributions of log price and log return. Integrating the Black–Scholes dynamics from the current time to maturity…

The document formulates a fit between a target time series and a linear combination of two other series. It minimizes the sum of absolute residuals, the L1 norm, while constraining both coefficients to lie between minus one and one. This differs from…

The discussion distinguishes PCA scores, which describe observations such as dates in principal-component space, from factor loadings, which describe each stock’s exposure to the components. It explains why clustering loadings may emphasize a component with…

The discussion asks whether a payer Bermudan swaption’s chance of exercise at its first exercise date rises or falls as interest rates increase. Its answer gives an intuitive example: for a payer option with a fixed strike and a flat curve, low swap rates…

The document explains that life insurers can face equity risk through both their investment portfolios and the products they sell. In the European Union, Solvency II does not impose a blanket ban on equity holdings. Instead, insurers must hold sufficient own…

The document explains a payoff decomposition for a secured barrier call. The product pays the positive difference between the terminal stock price and the strike if the upper barrier is never reached; if the stock reaches that barrier before expiration, it…

The document explains how to translate a USD Libor curve into an equivalent EUR funding curve. Its central method is to convert EUR into USD at spot, accrue the USD cash at the relevant Libor rate, and convert it back to EUR at a forward FX rate. Comparing…

The document asks whether a central bank's published government yield curve is a forecast of future policy rates or a curve derived from bond market prices. The context is the fall and steepening of UK gilt yields after the Brexit vote, which the question…

The discussion examines a reproduction example used to explain how risk aversion might become prevalent over generations. Risk-averse tribbles always have three offspring, while risk-neutral tribbles have either two or four with equal probability. The…

The document discusses estimating intraday liquidity at price levels to guide execution, rather than relying only on a time-based volume profile such as the U-shaped pattern used by a VWAP schedule. It suggests combining liquidity signals with a decision…

The document considers which volatility input to use when pricing options on futures with the Black model or a binomial tree. Its central point is that the appropriate volatility depends on the asset class and on which instrument provides the most relevant…

The document explains how risk-free rates affect long-short portfolio returns. If the long and short legs have equal funding amounts, subtracting the risk-free rate from each leg before combining them gives the same result as calculating the long-short…

The document discusses ways to detect hidden liquidity in a limit order book. One proposed signal is repeated trading at a best bid or ask while displayed size is replenished, or while the price repeatedly returns to the same level despite continuing buying…

The document asks whether the power-law tail exponent of log returns should remain the same when returns are aggregated from daily to longer horizons. It notes the theoretical argument that a regularly varying tail can preserve its exponent under…